Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
1340 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#5220 | C2 | semidirect |
| 3. C2×C5×#834 | C2 | semidirect |
| 6. C3×C5×H(5,𝔽2) | C4 | semidirect |
| 10. C23×C5×Dic3 | C22 | semidirect |
| 12. C2×C5×#217 | C22 | semidirect |
| 15. #72142 | C5 | direct (N × H) |
| 40. #5220 | C2×C5 | semidirect |
| 41. C2×#834 | C2×C5 | semidirect |
| 43. C5×H(5,𝔽2) | Dic3 | semidirect |
| 62. C23×C3×C5 | C22⋊C4 | semidirect |
| 73. C2×C3×C4×C5 | C22⋊C4 | semidirect |
| 81. C3×H(5,𝔽2) | C4×C5 | semidirect |
| 85. C23×Dic3 | C22×C5 | semidirect |
| 87. C2×#217 | C22×C5 | semidirect |
| 158. C23×C5 | #217 | semidirect |
| 175. C2×C4×C5 | #217 | semidirect |
| 177. H(5,𝔽2) | C5×Dic3 | semidirect |
| 201. C23×C3 | C5×C22⋊C4 | semidirect |
| 212. C2×C3×C4 | C5×C22⋊C4 | semidirect |
| 255. C3×C5 | #1790 | semidirect |
| 287. C23 | C5×#217 | semidirect |
| 304. C2×C4 | C5×#217 | semidirect |
| 311. C5 | #72142 | direct (N × H) |
| 328. C3 | C5×#1790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×H(5,𝔽2) | 2 |
| C5×#5220 | 2 |
| C2×C5×#834 | 2 |
| C5×#1790 | 3 |
| #72142 | 5 |